A Novel ADI-Weak Galerkin Method for Singularly Perturbed Two-Parameter 2D Parabolic Pdes

In this article, we propose an Alternating Direction Implicit (ADI) type operator splitting weak Galerkin finite element method (WG-FEM) for solving a parabolic singularly perturbed problem with two-parameters in 2D over a layer-adapted mesh. The suggested operator splitting approach divides the original model problem into two subproblems each in 1D, then solving each subproblem using WG-FEM in spatial direction eventually reduces the computational difficulty and high storage requirements. Backward-Euler time discretization has been taken over a uniform mesh. Stability and convergence results have been proved for the fully-discrete scheme. Numerical examples are presented corroborating in practice our theoretical findings.